Solve vector problems by resolving vectors into components, adding or subtracting the components and recombining them to determine the resultant vector.

A drone is moving with velocity 18.0 m s⁻¹ at 35.0° north of east. A steady wind applies an additional velocity of 8.50 m s⁻¹ at 125° measured anticlockwise from east. Determine the resultant velocity of the drone. Justify your answer by describing the resolution and recombination process you used.

A drone undergoes three consecutive displacement vectors during a delivery flight. It first travels \(\vec{d}_1 = 850\) m at \(35.0^\circ\) north of east, then \(\vec{d}_2 = 620\) m at \(115^\circ\) measured anticlockwise from east, and finally \(\vec{d}_3 = 480\) m directly south. Determine the magnitude and direction of the drone's resultant displacement from its starting position. Show your working.

A rescue helicopter is flying horizontally at 45.0 m s⁻¹ due east when it releases a supply package. At the instant of release, a ground observer measures a steady wind applying a horizontal force, giving the package a constant horizontal acceleration of 2.50 m s⁻² due south throughout its fall. The package takes 3.20 s to reach the ground. Determine the magnitude and direction of the package's velocity just before it strikes the ground. Justify your answer by resolving the velocity into components.